No it is not illegal to not have health insurance in New Jersey. Under the Patient Protection and Affordable Care Act of 2010 (PPACA, aka Obamacare) there will be a federal mandate to acquire health insurance that will result in penalty taxes imposed on income for individuals who do not acquire health insurance.

The extent of this penalty tax will decrease over the course of the next several years.

That is a great question! While it is not technically illegal to not have health insurance coverage, the Affordable Care Act (Obamacare) does impose penalties on those who choose to remain uninsured. The purpose behind having people insured is to greatly lower the costs of health care. When someone without insurance seeks medical care, the cost for that treatment is passed on to all the other people who seek treatment in the form of higher prices. Insuring them returns that cost to them, and the insurance company. Also adding more healthy people to the pool lowers costs, as there is more money going in, and less going out, lowering costs. I hope that helps, thanks for asking!